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It is well known that no satisfactory demonstration has ever been given of Fermat's celebrated theorem, which asserts that the equationan=bn+cnis impossible, ifa,b,c, are whole numbers, andnis any whole number greater than 2. In Legendre'sThéorie des Nombres, he demonstrates the cases ofn= 3,n= 4, andn= 5, the latter only in his Second Supplement. In Crelle'sMathematical Journal, ix. 390, M. Dirichlet, a mathematician of Berlin, has demonstrated the case ofn= 14, but I am not aware whether hisdoi:10.1017/s008045680003221x fatcat:ihulwiayhbdxfehq35wgmc5ftu